2 Answers
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If you ask the tour operator they will claim they use a Kitty system as it makes it easier to get the money to the tour operators and the passengers generally give it to them directly on day one, often in local currency or currency that can be used locally (such as US$). It also allows them to change the Kitty amount after the trip has been booked and paid for if local conditions change - ie, they are moving some of the risk of price fluctuations from the tour company to the passenger, even if the passenger did the right thing and booked and paid early.

If you ask most tour passengers, it's simply a way for them to make the trip look cheaper. Rather than advertising a tour as being $2000, they can advertise it as being $1500, and then in the small print mention that there's a $500 kitty payable.

If you ask a travel agent, they will tell you that the kitty is a way of the tour company avoiding paying them commission. Travel agents will normally earn a percentage of the price paid for a trip, but only of the component that is the actual "price" of the trip, not any extra components such as the kitty, so they miss out of commission of the kitty component.

Some companies seem to abuse this more than others - the specific example you've included in the question is a great example of that - the kitty price ends up being 40% of what you pay for the trip! In some countries (Australia, US) the tour companies are required to display the "full" price at time of booking, so the kitty payment is at least clear before booking, but in other countries it's not uncommon for the kitty price to not be clearly displayed, and it can some as quite a shock to some people when they find out about it after booking!

Quite some time ago I have been on a couple of such trips. Back then it was called a food kitty. Unlike the fixed amounts you are pointing to this was a per-week amount, although it was collected at the start. This is important as if the trip ran long (and both the trips I was on did) the passengers were expected to pay the weekly amount for the additional duration.

One other thing also comes to mind: I suspect there are tax advantages to doing it that way.